dorsal/arxiv
View SchemaOn the Monge-Ampere equivalent of the sine-Gordon equation
| Authors | E. V. Ferapontov, Y. Nutku |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9409004 |
| URL | https://arxiv.org/abs/solv-int/9409004 |
| DOI | 10.1088/0305-4470/27/23/026 |
Abstract
Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampere equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Backlund-type transformation between the sine-Gordon and Monge-Ampere equations.
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"abstract": "Surfaces of constant negative curvature in Euclidean space can be described\nby either the sine-Gordon equation for the angle between asymptotic directions,\nor a Monge-Ampere equation for the graph of the surface. We present the\nexplicit form of the correspondence between these two integrable non-linear\npartial differential equations using their well-known properties in\ndifferential geometry. We find that the cotangent of the angle between\nasymptotic directions is directly related to the mean curvature of the surface.\nThis is a Backlund-type transformation between the sine-Gordon and Monge-Ampere\nequations.",
"arxiv_id": "solv-int/9409004",
"authors": [
"E. V. Ferapontov",
"Y. Nutku"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1088/0305-4470/27/23/026",
"title": "On the Monge-Ampere equivalent of the sine-Gordon equation",
"url": "https://arxiv.org/abs/solv-int/9409004"
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